Why does the BOINC Manager every once in a while activate my DVD drive for a few seconds?

"every once in a while" - how often? (every few minutes, once a day?)

If you exit BOINC is there any difference?
Do you use default directories for BOINC (during installation)?

Is there any difference if a CD/DVD disk is inside or not?

(One of my older (computer) DVD drives activates by itself (no disk inside) - it thinks I press open/close button (most probably the internal sensor (button)).
Also my home DVD player (connected only to TV - not the computer) randomly ("once in a while") closes the tray just after eject
so I wait a few seconds before changing (removing, inserting) the disk.

All DVD drives/players have internal sensor (button) which activates the tray motor to "swallow" the disk if you push on the (opened) tray.
If this sensor is bad the drive may become active (even if it is now with closed tray)
as the drive thinks that you just closed the tray (and spins to check is there disk inside).
)